Question

Найти производную функции y=x^2*ln2x и обчислитьиы значение при x=0.5

Answer 1

(uv)' = u'v + uv'
u = x^2
v = ln2x
u' = 2x
v' = 1/x
(x^2*ln2x)' = 2x*ln2x + x = x(2ln2x+1)
0,5(2ln1+1) = 0,5(2*0+1)=0,5

Answer 2

y'=2x*ln2x+x^2* 1/2x * 2 = 2x*ln2x+x